Trigonometry Examples

$17496 \sqrt{2} \cdot \cos (315)$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$17496 \sqrt{2} \cdot \cos (45)$

Step 2

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$17496 \sqrt{2} \cdot \frac{\sqrt{2}}{2}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $17496 \sqrt{2}$ .

$2 (8748 \sqrt{2}) \cdot \frac{\sqrt{2}}{2}$

Step 3.2

Cancel the common factor.

$2 (8748 \sqrt{2}) \cdot \frac{\sqrt{2}}{2}$

Step 3.3

Rewrite the expression.

$8748 \sqrt{2} \cdot \sqrt{2}$

Step 4

Raise $\sqrt{2}$ to the power of $1$ .

$8748 ({\sqrt{2}}^{1} \sqrt{2})$

Step 5

Raise $\sqrt{2}$ to the power of $1$ .

$8748 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8748 {\sqrt{2}}^{1 + 1}$

Step 7

Add $1$ and $1$ .

$8748 {\sqrt{2}}^{2}$

Step 8

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Step 8.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$8748 {(2^{\frac{1}{2}})}^{2}$

Step 8.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8748 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 8.3

Combine $\frac{1}{2}$ and $2$ .

$8748 \cdot 2^{\frac{2}{2}}$

Step 8.4

Cancel the common factor of $2$ .

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Step 8.4.1

Cancel the common factor.

$8748 \cdot 2^{\frac{2}{2}}$

Step 8.4.2

Rewrite the expression.

$8748 \cdot 2^{1}$

Step 8.5

Evaluate the exponent.

$8748 \cdot 2$

Step 9

Multiply $8748$ by $2$ .

$17496$